Fluctuation-stable generalized entropy probes of spectral heterogeneity
arXiv:2606.08801 · doi:10.1016/j.physleta.2026.131989
The paper develops a theoretical framework showing that generalized entropy measures are more stable for q>1, introduces an entropy-gradient susceptibility to detect spectral heterogeneity, and applies it to quasiperiodic models.
Abstract
Generalized entropy measures are widely used to characterize localization and multifractality, and the regime \(q>1\) is often empirically found to exhibit improved numerical stability and cleaner scaling behavior. Here, we develop a fluctuation-stability framework for generalized entropy diagnostics and show that weak-amplitude spectral fluctuations are amplified for \(q<1\) and suppressed for \(q>1\), thereby providing a theoretical basis for the physically robust \(q>1\) regime. A thermodynamic scaling analysis further identifies an asymptotically stable regime beyond a critical threshold. As an application, we introduce the entropy-gradient susceptibility \(Ï_q\) as a coarse-grained probe of spectral heterogeneity. Using the Aubry-André and generalized Aubry-André models, we demonstrate that \(Ï_q\) sharply distinguishes homogeneous localization transitions from mobility-edge coexistence regimes. Our results establish fluctuation stability as a guiding principle for generalized entropy diagnostics in quasiperiodic systems.
Final version: 9 pages, 3 figures, Accepted for publication in Phys. Lett. A